Improving Engineering Design with Fuzzy Sets

The Method of Imprecision (MoI) is a formal method, utilizing the mathematics of fuzzy sets, for incorporating the natural level of imprecision that occurs throughout the engineering design process. This paper presents the details of the Level Interval Algorithm (LIA) used internally by the MoI, and its extensions to permit application to engineering design problems in industry where monotonicity cannot be guaranteed, only discrete values may be available for some variables (and hence continuity must be relaxed), and engineering analyses are expensive and must be minimized. Computation problems that reach beyond the scope of the LIA, such as singularities, etc., are also examined, showing that the LIA behaves no worse than conventional calculations in the presence of these difficulties.